| Summary: | 博士 === 國立臺灣大學 === 電機工程學研究所 === 102 === This dissertation studies a general class of linear systems with multiple successive delay components. First of all, the delays are assumed to vary in intervals, and delay-dependent exponential stability conditions are derived in terms of linear matrix inequalities. To reduce conservativeness, a new Lyapunov-Krasovskii functional is designed to contain more complete state information, so that a derivation procedure with time-varying delays treated as uncertain parameters can be adopted. Secondly, when the lower bound of time-varying delay’s rate of change is greater than or equal to zero, a delay-parameter-dependent Lyapunov functional is built to analyze the stability of linear systems with a non-decreasing time-varying delay. Pure numerical examples as well as an example with a DC motor model are provided to demonstrate the effectiveness of the proposed stability criteria.
Finally, a digital quasi-PD controller is proposed to achieve exponential stabilization for linear continuous-time systems. As a variation of the traditional position and delayed position (PDP) control, the proposed controller uses samples of the output signals, which is easier to implement and more practical. A second-order negatively damped system and a double inverted pendulum system are tested to show the control method is effective.
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